This method is used to solve the problem in the domain with a boundary location unknown in advance. Method allows to have this interface exactly at the finite element boundaries . It is important if material properties exhibit step variation, like solid-liquid interface, liquid-void etc.

The idea of this original approach (IFEM) has been proposed by A.N. Alexandrou (Int. J. Numer. Meth. Eng., 28, 1989, 2383). We have done important modification of the method and extended it to include more general boundary conditions (A.I. Fedoseyev, J. I. D. Alexander, J. Comp. Phys., 130, 1997, 243). The latter includes the explicit presence of an ampoule (with a complex shape) that contains the solid and the melt from which it is growing. Heat transfer between the ampoule and the external environment, time dependent boundary conditions, nonmonotonic temperature distributions, and species diffusion in the melt and crystal are also taken into account. Thus, our extended formulation encompasses a wider class of solidification problems than previous IFEM methods.

The problem of directional solidification (Bridgman technique) is used as an example.
Here is typical ampoule geometry and related computational domain:

Geometry and domain

Boundary temperature is taken from the experimental data (thermocouples at A, B, C, ... G for the USML-2 flight). Here we present the interface shape and location versus time from numerical experiments that we have done.

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7/5/99

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